We propose a simple scenario of dynamical supersymmetry breaking in four-dimensional supergravity theories. The supersymmetry breaking sector is assumed to be completely separated as a sequestered sector from the visible sector, except for communication by gravity and U(1)R gauge interactions, and supersymmetry breaking is mediated by the superconformal anomaly and U(1)R gauge interaction. Supersymmetry is dynamically broken by the interplay between the nonperturbative effect of the gauge interaction and the Fayet-Iliopoulos D term of U(1)R which necessarily exists in supergravity theories with gauged U(1)R symmetry. We construct an explicit model which gives a phenomenologically acceptable mass spectrum of superpartners with a vanishing (or very small) cosmological constant.